Optimal. Leaf size=47 \[ -\frac{F^a (c+d x) \text{Gamma}\left (\frac{1}{3},-b \log (F) (c+d x)^3\right )}{3 d \sqrt [3]{-b \log (F) (c+d x)^3}} \]
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Rubi [A] time = 0.0070726, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {2208} \[ -\frac{F^a (c+d x) \text{Gamma}\left (\frac{1}{3},-b \log (F) (c+d x)^3\right )}{3 d \sqrt [3]{-b \log (F) (c+d x)^3}} \]
Antiderivative was successfully verified.
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Rule 2208
Rubi steps
\begin{align*} \int F^{a+b (c+d x)^3} \, dx &=-\frac{F^a (c+d x) \Gamma \left (\frac{1}{3},-b (c+d x)^3 \log (F)\right )}{3 d \sqrt [3]{-b (c+d x)^3 \log (F)}}\\ \end{align*}
Mathematica [A] time = 0.0160868, size = 47, normalized size = 1. \[ -\frac{F^a (c+d x) \text{Gamma}\left (\frac{1}{3},-b \log (F) (c+d x)^3\right )}{3 d \sqrt [3]{-b \log (F) (c+d x)^3}} \]
Antiderivative was successfully verified.
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Maple [F] time = 0.017, size = 0, normalized size = 0. \begin{align*} \int{F}^{a+b \left ( dx+c \right ) ^{3}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int F^{{\left (d x + c\right )}^{3} b + a}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.5441, size = 157, normalized size = 3.34 \begin{align*} \frac{\left (-b d^{3} \log \left (F\right )\right )^{\frac{2}{3}} F^{a} \Gamma \left (\frac{1}{3}, -{\left (b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3}\right )} \log \left (F\right )\right )}{3 \, b d^{3} \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int F^{a + b \left (c + d x\right )^{3}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int F^{{\left (d x + c\right )}^{3} b + a}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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